Two General Extension Algorithms of Latin Hypercube Sampling

Abstract

For reserving original sampling points to reduce the simulation runs, two general extension algorithms of Latin Hypercube Sampling (LHS) are proposed. The extension algorithms start with an original LHS of sizemand construct a new LHS of sizem+nthat contains the original points as many as possible. In order to get a strict LHS of larger size, some original points might be deleted. The relationship of original sampling points in the new LHS structure is shown by a simple undirected acyclic graph. The basic general extension algorithm is proposed to reserve the most original points, but it costs too much time. Therefore, a general extension algorithm based on greedy algorithm is proposed to reduce the extension time, which cannot guarantee to contain the most original points. These algorithms are illustrated by an example and applied to evaluating the sample means to demonstrate the effectiveness.